Fuel gage not working

Yes the fuel tank has to come out to change the fuel pump. But are you sure that is the problem ? Your vehicle has a Fuel Pump Flow Control Module (electronic's ) Or is it just your fuel level sensor you want to replace ? And to your question of if the fuel level sensor is bad will the car shut down if the gage says it is emty but it is not? No ,this will not shut down the vehicle. You probably have no idea of the complexity of the electronic's involved an the thing's that can cause the gauge not to work .
Fuel Gage
The instrument panel cluster (IPC) displays the fuel level as determined by the ECM. The IPC receives a serial data message from the ECM indicating the fuel level percent. The fuel gage defaults to empty if:
• The ECM detects a malfunction in the fuel level sensor circuit.
• The IPC detects a loss of serial data communications with the BCM
• The BCM detects a loss of serial data communications with the ECM
When the fuel level is less than a pre-determined value, the low fuel indicator illuminates in the IPC.
Unless you have a factory or professional type scan tool your better off taking your vehicle to a qualified repair shop.

Fuel Gage Inaccurate or Inoperative
Circuit/System Description
The fuel level sender changes resistance based on the fuel level. The engine control module (ECM) monitors the signal circuit of the fuel level sender to determine fuel level. When the fuel tank is full, the sender resistance is low and the ECM senses a low signal voltage. When the fuel tank is empty, the sender resistance is high and the ECM senses a high signal voltage. The ECM uses the signal circuit of the fuel level sender in order to calculate the remaining fuel level percent in the tank. The ECM sends the fuel level message via the serial data circuit to the body control module (BCM). The BCM sends the fuel level percent to the instrument panel cluster (IPC) via the serial data circuit for display on the fuel gage.

Circuit
Short to Ground
High Resistance
Open
Short to Voltage
Signal Performance
Fuel Level Sensor Signal
P0462
1
P0463, P0464
P0463
P0461
Fuel Level Sensor Low Reference
--
1
P0463, P0464
P0463
P0461
1. Fuel Gage Inaccurate or Inoperative

Do you know what a DTC is ? diagnostic trouble code !

Could be the gage or the sender unit. Have someone take the wire off the sender unit at the fuel tank and touch it to ground If the gage goes to full tank the replace the sender unit. Could also be a broken wire from the gage to sender

check power to the sender unit in the fuel tank may be a break in the wire in your trunk/boot. if not change the sender unit.

Check your fuse firstly.If that's ok, then check and clean the wires at the plug on the fuel tank.If no joy then your sender unit in the tank has failed.Remove the plug on the fuel tank and short out the wires and check to see if the Gage works.if so its not the Gage,its def the sender in the tank.

The fuel gage or the fuel sender unit inside fuel tank.
the sender unit is hard to check because is in the fuel tank.
the gage is easier, remove the cluster with the key on connect and disconnect the 2 connectors in the back of the cluster if the gage moves the problem is the sender unit inside the fuel tank.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/flavio_517b938f50183b92

The most common cause of a erratic or incorrect fuel gage reading is a defective fuel gage sending unit inside the fuel tank. To replace the sending unit requires that the fuel tank be removed from the car and then the fuel pump module which contains the sender be replaced.

Perhaps you might consider the sending unit in the gas tank.

there is a sender in the fule tank this may be faulty so its not sending the info to the tank gage find the whire from this sender on the fule tank and short it out to the car bodywork the tank should then read full up if the wireing is good, if there is still no reading its likley to be the gage not working, or a broken wire to the sender,,,if the sender is broken it canot be fixed so fit a new one but check how much fule is in the tank before you try to remove the old sender or it may spill out every were, if you fit a new selder only add a gall of fule and see if there is a reading on the gage before adding more so you find out when the tank is realy empty,, never trust the gage to be true

They could have installed the wrong pump assembly. I would first check to see if the float arm is binding on something not allowing it to reach the empty position. If you take the assembly out, have the key onand work the sender up and down thru its travel and see if the gauge matches the sender position. Disconnect the wire going to the pump so it doesn't get damaged.

see if there is any acces to the fuel tank cover under the rear seat, if it is then remove the screws and remove the sending unit sending unit inside the tank most likelly it will be bad, but if you don't feel like doing it, then take it to your mechanic but seems to be the sending unit inside the tank wich is the sensor trigering your gage is not good and need to be tested and replaced